Demonstration of AI-Assisted Scientific Workflow on Canonical Benchmarks

Abstract: We present a fully reproducible demonstration of an AI-assisted scientific workflow designed for a broad physics, mathematics, and computer-science readership. The initial project artifact stack was generated from one single user prompt and then reviewed and curated for submission by the human author. Rather than claiming a new scientific discovery, the manuscript uses canonical benchmark problems with exact, manufactured, or independently checkable answers. The analytical component starts from the one-dimensional quantum harmonic oscillator, derives its dimensionless form, and validates finite-difference eigenpairs against exact Hermite-function benchmarks. The numerical partial-differential-equation component solves a heat equation with a known modal solution and a Poisson problem verified by a manufactured solution, with explicit convergence studies. The inverse-modeling component fits synthetic damped-oscillation data by nonlinear least squares and quantifies parametric uncertainty by bootstrap resampling. The computational-science component compares dense and sparse eigensolvers and contrasts direct and iterative sparse linear solvers, with careful interpretation of machine-dependent timing data. Taken together, the results show that contemporary AI can already serve as a useful scientific copilot for derivation, implementation, validation, visualization, and manuscript preparation, provided that each stage is constrained by benchmark theory, explicit verification, and transparent artifacts. The demonstration is therefore relevant not because the underlying science is novel, but because it offers a concrete template for trustworthy AI use in technical research practice.